From 2c2da2775252b66ec4383c582cb6e1efc64cae11 Mon Sep 17 00:00:00 2001 From: "matthias@quintern.xyz" Date: Sat, 30 Nov 2024 16:50:47 +0100 Subject: [PATCH] fixes --- src/atom.tex | 1 - src/condensed_matter.tex | 68 ++++++------------- src/electrodynamics.tex | 62 +++++++++++++---- src/main.tex | 93 +++++++++++++++++++++---- src/many-body-simulations.tex | 10 --- src/maths/analysis.tex | 4 +- src/mechanics.tex | 12 ++++ src/quantum_computing.tex | 41 ++++++----- src/quantum_mechanics.tex | 79 +++++++++++++++++----- src/statistical_mechanics.tex | 2 +- src/svgs/convertToPdf.sh | 0 src/topo.tex | 8 ++- src/util/environments.tex | 124 ++++++++++++++++++++++++++-------- src/util/macros.tex | 2 + src/util/translation.tex | 20 ++++-- 15 files changed, 361 insertions(+), 165 deletions(-) mode change 100755 => 100644 src/main.tex delete mode 100644 src/many-body-simulations.tex mode change 100644 => 100755 src/svgs/convertToPdf.sh diff --git a/src/atom.tex b/src/atom.tex index 6b4c059..043b47a 100644 --- a/src/atom.tex +++ b/src/atom.tex @@ -178,5 +178,4 @@ \ger{Effekte im Magnetfeld} ]{mag_effects} \TODO{all} - \\\TODO{Hunds rules} diff --git a/src/condensed_matter.tex b/src/condensed_matter.tex index cdaa504..812d940 100644 --- a/src/condensed_matter.tex +++ b/src/condensed_matter.tex @@ -85,6 +85,8 @@ \end{tabularx} \end{adjustbox} \end{table} + \TODO{FCC, BCC, diamond/Zincblende wurtzize cell/lattice vectors} + \TODO{primitive unit cell: contains one lattice point}\\ family of plane that are equivalent due to crystal symmetry \begin{formula}{miller} @@ -254,6 +256,26 @@ family of plane that are equivalent due to crystal symmetry \TODO{TODO} +\Section[ + \eng{Semiconductors} + \ger{Halbleiter} +]{semic} + \begin{formula}{charge_density_eq} + \desc{Equilibrium charge densitites}{}{} + \desc[german]{Ladungsträgerdichte im Equilibrium}{}{} + \eq{ + n_0 &\approx N_\text{c}(T) e^{-\frac{E_\text{c} - \EFermi}{\kB T}} \\ + p_0 &\approx N_\text{v}(T) e^{-\frac{\EFermi - E_\text{v}}{\kB T}} + } + \end{formula} + \begin{formula}{charge_density_intrinsic} + \desc{Intrinsic charge density}{}{} + \desc[german]{Intrinsische Ladungsträgerdichte}{}{} + \eq{ + n_\text{i} \approx \sqrt{n_0 p_0} = \sqrt{N_\text{c}(T) N_\text{v}(T)} e^{-\frac{E_\text{gap}}{2\kB T}} + } + \end{formula} + \Section[ \eng{Measurement techniques} \ger{Messtechniken} @@ -408,49 +430,3 @@ family of plane that are equivalent due to crystal symmetry \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf} \end{minipage} -\Section[ - \eng{Superconductivity} - \ger{Supraleitung} -]{sc} - \begin{ttext} - \eng{ - Materials for which the electric resistance jumps to 0 under a critical temperature. - \\\textbf{Type I}: Has a single critical magnetic field at which the superconuctor becomes a normal conductor. - \\\textbf{Type II}: Has two critical - } - \ger{Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur auf 0 springt.} - \end{ttext} - - \begin{formula}{meissner_effect} - \desc{Meißner-Ochsenfeld effect}{Perfect diamagnetism}{} - \desc[german]{Meißner-Ochsenfeld Effekt}{Perfekter Diamagnetismus}{} - \ttxt{ - \eng{Blabla } - \ger{Blubb blubb } - } - \end{formula} - \Subsection[ - \eng{London equation} - \ger{London-Gleichungen} - ]{london} - \begin{formula}{first} - % \vec{j} = \frac{nq\hbar}{m}\Grad S - \frac{nq^2}{m}\vec{A} - \desc{First London Equation}{}{$\vec{j}$ current density, $n$, $m$, $q$ density, mass and charge of superconduticng particles} - \desc[german]{Erste London-Gleichung}{}{$\vec{j}$ Stromdichte, $n$, $m$, $q$ Dichte, Masse und Ladung der supraleitenden Teilchen} - \eq{ - \partical_t \vec{j} = \frac{nq^2}{m}\vec{E} - } - \end{formula} - \begin{formula}{second} - \desc{Second London Equation}{}{$\vec{j}$ current density, $n$, $m$, $q$ density, mass and charge of superconduticng particles} - \desc[german]{Zweite London-Gleichung}{}{$\vec{j}$ Stromdichte, $n$, $m$, $q$ Dichte, Masse und Ladung der supraleitenden Teilchen} - \eq{ - \Rot \vec{j} = -\frac{nq^2}{m} \vec{B} - } - \end{formula} - \begin{formula}{penetration_depth} - \desc{London penetration depth}{}{} - \desc[german]{London Eindringtiefe}{}{} - \eq{\lambda_\textrm{L} = \sqrt{\frac{m}{\mu_0 nq^2}}} - \end{formula} - diff --git a/src/electrodynamics.tex b/src/electrodynamics.tex index a97d133..a402304 100644 --- a/src/electrodynamics.tex +++ b/src/electrodynamics.tex @@ -42,7 +42,7 @@ \Subsection[ \eng{Electric field} \ger{Elektrisches Feld} - ]{mag} + ]{el} \begin{formula}{gauss_law} \desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface} \desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche} @@ -57,11 +57,10 @@ \Eng[magnetic_flux]{Magnetix flux density} \Ger[magnetic_flux]{Magnetische Flussdichte} - % \begin{quantity}{mag_flux}{\Phi}{\Wb}{\kg\m^2\per\s^2\A^1}{scalar} - % \sign{} - % \desc{Magnetic flux density}{} - % \desc[german]{Magnetische Feldstärke}{} - % \end{quantity} + \begin{quantity}{mag_flux}{\Phi}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar} + \desc{Magnetic flux}{} + \desc[german]{Magnetischer Fluss}{} + \end{quantity} \begin{formula}{magnetic_flux} \desc{Magnetic flux}{}{} @@ -75,11 +74,6 @@ \eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0} \end{formula} - \begin{formula}{name} - \desc{}{}{} - \desc[german]{}{}{} - \eq{} - \end{formula} \begin{formula}{magnetization} \desc{Magnetization}{}{$m$ mag. moment, $V$ volume} \desc[german]{Magnetisierung}{}{$m$ mag. Moment, $V$ Volumen} @@ -109,7 +103,7 @@ \Subsection[ \eng{Induction} - \ger{Unduktion} + \ger{Induktion} ]{induction} \begin{formula}{farady_law} \desc{Faraday's law of induction}{}{} @@ -117,6 +111,19 @@ \eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}} \end{formula} + \begin{formula}{lenz} + \desc{Lenz's law}{}{} + \desc[german]{Lenzsche Regel}{}{} + \ttxt{ + \eng{ + Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux. + } + \ger{ + Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt. + } + } + \end{formula} + \Section[ \eng{Hall-Effect} \ger{Hall-Effekt} @@ -160,7 +167,7 @@ \Subsection[ \eng{Integer quantum hall effect} \ger{Ganzahliger Quantenhalleffekt} - ]{quantum} + ]{quantum} \begin{formula}{conductivity} \desc{Conductivity tensor}{}{} @@ -178,8 +185,8 @@ \end{formula} \begin{formula}{resistivity} - \desc{Resistivity}{}{$\nu \in \mathbb{Z}$} - \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$} + \desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor} + \desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor} \eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}} \end{formula} @@ -188,6 +195,31 @@ % \desc[german]{Ganzahliger Quanten-Hall-Effekt}{}{} % \fig{img/qhe-klitzing.jpeg} % \end{formula} + + \begin{formula}{fqhe} + \desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors} + \desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler} + \eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...} + \end{formula} + + \begin{ttext} + \eng{ + \begin{itemize} + \item \textbf{Integer} (QHE): filling factor $\nu$ is an integer + \item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction + \item \textbf{Spin} (QSHE): spin currents instead of charge currents + \item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields + \end{itemize} + } + \ger{ + \begin{itemize} + \item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig + \item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch + \item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme + \item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld + \end{itemize} + } + \end{ttext} \TODO{sort} diff --git a/src/main.tex b/src/main.tex old mode 100755 new mode 100644 index 2fd220c..8793639 --- a/src/main.tex +++ b/src/main.tex @@ -36,6 +36,11 @@ \usepackage{tikz} % drawings \usetikzlibrary{decorations.pathmorphing} \usetikzlibrary{calc} +% speed up compilation by externalizing figures +% \usetikzlibrary{external} +% \tikzexternalize[prefix=tikz_figures] +% \tikzexternalize + \usepackage{circuitikz} % SCIENCE PACKAGES @@ -114,7 +119,13 @@ % Make the translation of #1 a reference to a equation % 1: key \newcommand{\fqEqRef}[1]{ - \hyperref[eq:#1]{\GT{#1}} + \edef\fqeqrefname{\GT{#1}} + \hyperref[eq:#1]{\fqeqrefname} +} +\newcommand{\qtyRef}[1]{ + % using temp edef so that underscores in undefined trasnlation keys are printed as characters + \edef\qtyrefname{\GT{qty:#1}} + \hyperref[qty:#1]{\qtyrefname} } % Make the translation of #1 a reference to a section % 1: key @@ -136,6 +147,7 @@ \input{util/macros.tex} \input{util/environments.tex} +% \includeonly{computational} \begin{document} \maketitle @@ -145,29 +157,80 @@ \input{util/translations.tex} -\input{maths/linalg.tex} -\input{maths/geometry.tex} -\input{maths/analysis.tex} -\input{maths/probability_theory.tex} +% \include{maths/linalg} +% \include{maths/geometry} +% \include{maths/analysis} +% \include{maths/probability_theory} -\input{mechanics.tex} +\include{mechanics} -\input{statistical_mechanics.tex} +\include{statistical_mechanics} -\input{electrodynamics.tex} +\include{electrodynamics} -\input{quantum_mechanics.tex} -\input{atom.tex} +\include{quantum_mechanics} +\include{atom} -\input{condensed_matter.tex} +\include{condensed_matter} +\include{low_temp} -\input{topo.tex} +\include{topo} -\input{quantum_computing.tex} +\include{quantum_computing} -% \input{many-body-simulations.tex} +\include{computational} -%\newpage +\include{quantities} + +\newpage +% \DT[english]{ttest}{TESTT EN} +% \DT[german]{ttest}{TESTT DE} + +\addtranslation{english}{ttest}{JA MOIN} +\noindent +GT: ttest = \GT{ttest}\\ +GetTranslation: ttest = \GetTranslation{ttest}\\ +Is english? = \IfTranslation{english}{ttest}{yes}{no} \\ +Is german? = \IfTranslation{german}{ttest}{yes}{no} \\ +Is defined = \IfTranslationExists{ttest}{yes}{no} \\ + +\def\ttest{NAME} +% \addtranslation{english}{\ttest:name}{With variable} +% \addtranslation{german}{\ttest:name}{Mit Variable} +% \addtranslation{english}{NAME:name}{Without variable} +% \addtranslation{german}{NAME:name}{Without Variable} +\DT[\ttest:name]{english}{DT With variable} +\DT[\ttest:name]{german}{DT Mit Variable} +\noindent +GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\ +GetTranslation: {\textbackslash}ttest:name = \GetTranslation{\ttest:name}\\ +Is english? = \IfTranslation{english}{\ttest:name}{yes}{no} \\ +Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\ +Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\ +Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no} + +% \DT[qty:test]{english}{HAHA} + +{blablabla \label{test}} + +\hyperref[test]{TEST reference} +\qtyRef{test} + +\DT[qty:test]{english}{HAHA} + + +\qtyRef{mass} +\GT{qty:#1} +\GT{\qtyname} + +\newpage +\Eng[appendix]{Appendix} +\Ger[appendix]{Anhang} +\part*{\GT{appendix}} +% \listofmyenv +\listofquantities +\listoffigures +\listoftables % \bibliographystyle{plain} % \bibliography{ref} \end{document} diff --git a/src/many-body-simulations.tex b/src/many-body-simulations.tex deleted file mode 100644 index 9b1aab4..0000000 --- a/src/many-body-simulations.tex +++ /dev/null @@ -1,10 +0,0 @@ -\Part[ - \eng{Many-body simulations} - \ger{Vielteilchen Simulationen} -]{mbsim} - - \Section[ - \eng{Importance sampling} - \ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit} - ]{importance_sampling} - diff --git a/src/maths/analysis.tex b/src/maths/analysis.tex index 3cc720f..704356e 100644 --- a/src/maths/analysis.tex +++ b/src/maths/analysis.tex @@ -125,8 +125,8 @@ \end{formula} \begin{formula}{error-function} - \desc{Error function}{\erf: \C \to \C}{} - \desc[german]{Fehlerfunktion}{Error function: \erf: \C \to \C}{} + \desc{Error function}{$\erf: \C \to \C$ and complementary error function $\erfc$}{} + \desc[german]{Fehlerfunktion}{$\erf: \C \to \C$ und komplementäre Fehlerfunktion $\erfc$}{} \eq{ \erf(x) &= \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \d t \\ \erfc(x) &= 1 - \erf(x)\\ diff --git a/src/mechanics.tex b/src/mechanics.tex index f2dc4ee..c805f05 100644 --- a/src/mechanics.tex +++ b/src/mechanics.tex @@ -3,6 +3,18 @@ \ger{Mechanik} ]{mech} +\Section[ + \eng{Misc} + \ger{Verschiedenes} +]{misc} + \begin{formula}{hook} + \desc{Hooke's law}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ spring length} + \desc[german]{Hookesches Gesetz}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ Federlänge} + \eq{ + F = D\Delta l + } + \end{formula} + \def\lagrange{\mathcal{L}} \Section[ \eng{Lagrange formalism} diff --git a/src/quantum_computing.tex b/src/quantum_computing.tex index bc65405..967c37f 100644 --- a/src/quantum_computing.tex +++ b/src/quantum_computing.tex @@ -94,9 +94,9 @@ \desc[german]{SQUID}{Superconducting quantum interference device, besteht aus parralelen \hyperref{sec:qc:scq:josephson_junction}{Josephson Junctions} und kann zur Messung extrem schwacher Magnetfelder genutzt werden}{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} \draw (0, 0) \squidloop{loop}{}; - \end{circuitikz} + \end{tikzpicture} } \end{formula} \begin{formula}{hamiltonian} @@ -109,7 +109,7 @@ \eng{Josephson Qubit??} \ger{TODO} ]{josephson_qubit} - \begin{circuitikz} + \begin{tikzpicture} \draw (0,0) to[capacitor] (0,2); \draw (0,0) to (2,0); \draw (0,2) to (2,2); @@ -117,10 +117,10 @@ \draw[->] (3,1) -- (4,1); \draw (5,0) to[josephsoncap=$C_\text{J}$] (5,2); - \end{circuitikz} + \end{tikzpicture} \TODO{Include schaltplan} - \begin{circuitikz} + \begin{tikzpicture} \draw (0,0) to[sV=$V_\text{g}$] (0,2); \draw (0,2) to[capacitor=$C_\text{g}$] (2,2); \draw (2,2) to (4,2); @@ -128,7 +128,7 @@ \draw (4,0) to[capacitor=$C_C$] (4,2); \draw (0,0) to (2,0); \draw (2,0) to (4,0); - \end{circuitikz} + \end{tikzpicture} \begin{formula}{charging_energy} \desc{Charging energy / electrostatic energy}{}{} @@ -219,13 +219,13 @@ }{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} \draw (0,0) to[sV=$V_\text{g}$] (0,2); % \draw (0,0) to (2,0); \draw (0,2) to[capacitor=$C_\text{g}$] (2,2); \draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2); \draw (0,0) to (2,0); - \end{circuitikz} + \end{tikzpicture} } \end{formula} @@ -258,12 +258,12 @@ }{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3) % to[capacitor=$C_\text{g}$] ++(2,0) \draw (0,0) to ++(2,0) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to ++(0,-0.5) to ++(-2,0) to[capacitor=$C_C$] ++(0,3); - \end{circuitikz} + \end{tikzpicture} } \end{formula} @@ -282,14 +282,13 @@ \desc[german]{}{Durch Nutzung eines \fqSecRef{qc:scq:elements:squid} anstatt eines \fqSecRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3) % to[capacitor=$C_\text{g}$] ++(2,0) \draw (0,0) to ++(-2,0) to ++(3,0) to ++(0,-0.5) \squidloop{loop}{SQUID} to ++(0,-0.5) to ++(-3,0) to[capacitor=$C_C$] ++(0,3); - - \end{circuitikz} + \end{tikzpicture} } \end{formula} @@ -321,7 +320,7 @@ \desc[german]{Phase Qubit}{}{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3) % to ++(2,0) coordinate(top1) % to ++(2,0) coordinate(top2) @@ -335,7 +334,7 @@ \draw(0,0) to ++(2,0) to[josephsoncap=$C_\text{J}$] ++(0,-2) to ++(-2,0); \draw (2,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-2) to ++(-2,0); \node at (3,-1.5) {$\Phi_\text{ext}$}; - \end{circuitikz} + \end{tikzpicture} \\\TODO{Ist beim Fluxonium noch die Voltage source dran?} } \end{formula} @@ -361,15 +360,15 @@ \desc[german]{Flux Qubit / Persistent current qubit}{}{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} \draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3); \draw (0,0) to ++(3,0) to[josephsoncap=$E_\text{J}$] ++(0,-1.5) to[josephsoncap=$E_\text{J}$] ++(0,-1.5) to ++(-3,0); \node at (1.5,-1.5) {$\Phi_\text{ext}$}; - \end{circuitikz} - % \begin{circuitikz} + \end{tikzpicture} + % \begin{tikzpicture} % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3) % to ++(2,0) coordinate(top1) % to ++(2,0) coordinate(top2) @@ -385,7 +384,7 @@ % to[josephsoncap=$E_\text{J}$] ++(0,-1.5) % to[josephsoncap=$E_\text{J}$] (bot3); % \node at (5,0.5) {$\Phi_\text{ext}$}; - % \end{circuitikz} + % \end{tikzpicture} } \end{formula} @@ -406,14 +405,14 @@ }{} \content{ \centering - \begin{circuitikz} + \begin{tikzpicture} % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3) % to ++(2,0) coordinate(top1); \draw[color=gray] (0,0) to ++(-2,0) to[capacitor=$C_C$] ++(0,-3) to ++(2,0); \draw (0,0) to[josephsoncap=$C_\text{J}$] ++(-0,-3); \draw (0,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0); \node at (1,-0.5) {$\Phi_\text{ext}$}; - \end{circuitikz} + \end{tikzpicture} \\\TODO{Ist beim Fluxonium noch die Voltage source dran?} } \end{formula} diff --git a/src/quantum_mechanics.tex b/src/quantum_mechanics.tex index ef487e4..ba25ee5 100644 --- a/src/quantum_mechanics.tex +++ b/src/quantum_mechanics.tex @@ -211,6 +211,14 @@ \eq{\dot{\rho} = \underbrace{-\frac{i}{\hbar} [\hat{H}, \rho]}_\text{reversible} + \underbrace{\sum_{n.m} h_{nm} \left(\hat{A}_n\rho \hat{A}_{m^\dagger} - \frac{1}{2}\left\{\hat{A}_m^\dagger \hat{A}_n,\rho \right\}\right)}_\text{irreversible}} \end{formula} + \begin{formula}{hellmann_feynmann} + \desc{Hellmann-Feynman-Theorem}{Derivative of the energy to a parameter}{} + \desc[german]{Hellmann-Feynman-Theorem}{Abletiung der Energie nach einem Parameter}{} + \eq{ + \odv{E_\lambda}{\lambda} = \int \d^3r \psi^*_\lambda \odv{\hat{H}_\lambda}{\lambda} \psi_\lambda = \Braket{\psi(\lambda)|\odv{\hat{H}_{\lambda}}{\lambda}|\psi(\lambda)} + } + \end{formula} + \TODO{unitary transformation of time dependent H} @@ -250,15 +258,15 @@ ]{ehrenfest_theorem} \GT{see_also} \ref{sec:qm:basics:schroedinger_equation:correspondence_principle} \begin{formula}{ehrenfest_theorem} - \desc{Ehrenfesttheorem}{applies to both pictures}{} + \desc{Ehrenfest theorem}{applies to both pictures}{} \desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{} \eq{ \odv{}{t} \braket{\hat{A}} = \frac{1}{i\hbar}\braket{[\hat{A},\hat{H}]} + \Braket{\pdv{\hat{A}}{t}} } \end{formula} \begin{formula}{ehrenfest_theorem_x} - \desc{}{Example for $x$}{} - \desc[german]{}{Beispiel für $x$}{} + \desc{Ehrenfest theorem example}{Example for $x$}{} + \desc[german]{Ehrenfest-Theorem Beispiel}{Beispiel für $x$}{} \eq{m\odv[2]{}{t}\braket{x} = -\braket{\nabla V(x)} = \braket{F(x)}} \end{formula} % \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time} @@ -382,7 +390,26 @@ \begin{formula}{c_a_matrices} \desc{Matrix forms}{}{} \desc[german]{Matrix-Form}{}{} - \eq{\TODO{TODO}} + \eq{ + \hat{n} &= \begin{pmatrix} + 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \ddots & 0 \\ + 0 & 0 & 0 & N + \end{pmatrix} \\ + \hat{a} &= \begin{pmatrix} + 0 & \sqrt{1} & 0 & 0 \\ + 0 & 0 & \ddots & 0 \\ + 0 & 0 & 0 & \sqrt{N} \\ + 0 & 0 & 0 & 0 + \end{pmatrix} \\ + \hat{a}^\dagger &= \begin{pmatrix} + 0 & 0 & 0 & 0 \\ + \sqrt{1} & 0 & 0 & 0 \\ + 0 & \ddots & 0 & 0 \\ + 0 & 0 & \sqrt{N} & 0 + \end{pmatrix} + } \end{formula} \Subsubsection[ @@ -419,6 +446,21 @@ \eng{Angular momentum} \ger{Drehmoment} ]{angular_momentum} + + \Subsection[ + \eng{Aharanov-Bohm effect} + \ger{Aharanov-Bohm Effekt} + ]{aharanov_bohm} + \begin{formula}{phase} + \desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{} + \desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{} + \eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi} + \end{formula} + \TODO{replace with loop intergral symbol and add more info} + \Section[ + \eng{Periodic potentials} + \ger{Periodische Potentiale} + ]{periodic} \begin{formula}{bloch_waves} \desc{Bloch waves}{ Solve the stat. SG in periodic potential with period @@ -435,17 +477,6 @@ \eq{\psi_k(\vec{r}) = e^{i \vec{k}\cdot \vec{r}} \cdot u_{\vec{k}}(\vec{r})} \end{formula} - \Subsection[ - \eng{Aharanov-Bohm effect} - \ger{Aharanov-Bohm Effekt} - ]{aharanov_bohm} - \begin{formula}{phase} - \desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{} - \desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{} - \eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi} - \end{formula} - \TODO{replace with loop intergral symbol and add more info} - \Section[ \eng{Symmetries} @@ -488,7 +519,7 @@ \eq{H &= \underbrace{\hbar\omega_c \hat{a}^\dagger \hat{a}}_\text{\GT{field}} + \underbrace{\hbar\omega_\text{a} \frac{\hat{\sigma}_z}{2}}_\text{\GT{atom}} + \underbrace{\frac{\hbar\Omega}{2} \hat{E} \hat{S}}_\text{int} \\ - \shortintertext{\GT{after} \hyperref[eq:qm:other:RWS]{RWA}:} \\ + \shortintertext{\GT{after} \hyperref[eq:qm:other:RWA]{RWA}:} \\ &= \hbar\omega_c \hat{a}^\dagger \hat{a} + \hbar\omega_\text{a} \hat{\sigma}^\dagger \hat{\sigma} + \frac{\hbar\Omega}{2} (\hat{a}\hat{\sigma^\dagger} + \hat{a}^\dagger \hat{\sigma}) @@ -499,10 +530,24 @@ \eng{Other} \ger{Sonstiges} ]{other} - \begin{formula}{RWS} + \begin{formula}{RWA} \desc{Rotating Wave Approximation (RWS)}{Rapidly oscilating terms are neglected}{$\omega_\text{L}$ light frequency, $\omega_0$ transition frequency} \desc[german]{Rotating Wave Approximation / Drehwellennäherung (RWS)}{Schnell oscillierende Terme werden vernachlässigt}{$\omega_\text{L}$ Frequenz des Lichtes, $\omega_0$ Übergangsfrequenz} \eq{\Delta\omega \coloneq \abs{\omega_0 - \omega_\text{L}} \ll \abs{\omega_0 + \omega_\text{L}} \approx 2\omega_0} \end{formula} + \begin{formula}{slater_det} + \desc{Slater determinant}{Construction of a fermionic (antisymmetric) many-particle wave function from single-particle wave functions}{} + \desc[german]{Slater Determinante}{Konstruktion einer fermionischen (antisymmetrischen) Vielteilchen Wellenfunktion aus ein-Teilchen Wellenfunktionen}{} + \eq{ + \Psi(q_1, \dots, q_N) = \frac{1}{\sqrt{N!}} + \begin{vmatrix} + \phi_a(q_1) & \phi_a(q_2) & \cdots & \phi_a(q_N) \\ + \phi_b(q_1) & \phi_b(q_2) & \cdots & \phi_b(q_N) \\ + \vdots & \vdots & \ddots & \vdots \\ + \phi_z(q_1) & \phi_z(q_2) & \cdots & \phi_z(q_N) + \end{vmatrix} + } + \end{formula} + diff --git a/src/statistical_mechanics.tex b/src/statistical_mechanics.tex index 13d8f19..7f58208 100644 --- a/src/statistical_mechanics.tex +++ b/src/statistical_mechanics.tex @@ -746,7 +746,7 @@ \Subsubsection[ \eng{Strong degeneracy} \ger{Starke Entartung} - ]{degenerate} + ]{degenerate} \eng[low_temps]{for low temperatures $T \ll T_\text{F}$} \ger[low_temps]{für geringe Temperaturen $T\ll T_\text{F}$} diff --git a/src/svgs/convertToPdf.sh b/src/svgs/convertToPdf.sh old mode 100644 new mode 100755 diff --git a/src/topo.tex b/src/topo.tex index 6114510..27b68d5 100644 --- a/src/topo.tex +++ b/src/topo.tex @@ -67,7 +67,6 @@ \eq{C_n = \frac{1}{2\pi} \oint \d \vec{S}\ \cdot \vec{\Omega}_n(\vec{R})} \end{formula} - \TODO{Hall conductance of 2D band insulator (lecture 4 revision)} \begin{formula}{hall_conductance} \desc{Hall conductance of a 2D band insulator}{}{} \desc[german]{Hall-Leitfähigkeit eines 2D Band-Isolators}{}{} @@ -75,6 +74,9 @@ \end{formula} \begin{ttext} - \eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}} - + \eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}.} + \ger{Ein 2D Isolator mit einer Chernzahl ungleich 0 wird \textbf{topologischer Isolator} genannt.} \end{ttext} + + + diff --git a/src/util/environments.tex b/src/util/environments.tex index 26b5e92..48fce78 100644 --- a/src/util/environments.tex +++ b/src/util/environments.tex @@ -27,12 +27,12 @@ % 3: fqname of a translation that holds the explanation \newcommand{\NameWithExplanation}[3][\descwidth]{ \begin{minipage}{#1} - \iftranslation{#2}{ + \IfTranslationExists{#2}{ \raggedright - \gt{#2} - }{} - \iftranslation{#3}{ - \\ {\color{dark1} \gt{#3}} + \GT{#2} + }{NO NAME} + \IfTranslationExists{#3}{ + \\ {\color{dark1} \GT{#3}} }{} \end{minipage} } @@ -45,10 +45,10 @@ \begin{minipage}{#1} % \vspace{-\baselineskip} % remove the space that comes from starting a new paragraph #2 - \noindent\iftranslation{#3}{ + \noindent\IfTranslationExists{#3}{ \begingroup \color{dark1} - \gt{#3} + \GT{#3} % \edef\temp{\GT{#1_defs}} % \expandafter\StrSubstitute\expandafter{\temp}{:}{\\} \endgroup @@ -75,7 +75,7 @@ } \newcommand{\insertEquation}[2]{ - \NameLeftContentRight{#1}{ + \NameLeftContentRight{\fqname:#1}{ \begin{align} \label{eq:\fqname:#1} #2 @@ -84,7 +84,7 @@ } \newcommand{\insertFLAlign}[2]{ % eq name, #cols, eq - \NameLeftContentRight{#1}{% + \NameLeftContentRight{\fqname:#1}{% \begin{flalign}% % dont place label when one is provided % \IfSubStringInString{label}\unexpanded{#3}{}{ @@ -96,7 +96,7 @@ } \newcommand{\insertAlignedAt}[3]{ % eq name, #cols, eq - \NameLeftContentRight{#1}{% + \NameLeftContentRight{\fqname:#1}{% \begin{alignat}{#2}% % dont place label when one is provided % \IfSubStringInString{label}\unexpanded{#3}{}{ @@ -108,15 +108,16 @@ } \newcommand\luaexpr[1]{\directlua{tex.sprint(#1)}} -% 1: fqname -% 2: file path -% 3: equation +% [1]: width +% 2: fqname +% 3: file path +% 4: equation \newcommand{\insertEquationWithFigure}[4][0.55]{ \par\noindent\ignorespaces % \textcolor{gray}{\hrule} \vspace{0.5\baselineskip} \begin{minipage}{#1\textwidth} - \NameWithExplanation[\textwidth]{#2}{#2_desc} + \NameWithExplanation[\textwidth]{\fqname:#2}{#2_desc} % TODO: why is this ignored \vspace{1.0cm} % TODO: fix box is too large without 0.9 @@ -171,11 +172,11 @@ } % 1: any content \newcommand{\content}[1]{ - \NameLeftContentRight{#1}{##1} + \NameLeftContentRight{\fqname:#1}{##1} } % 1: content for the ttext environment \newcommand{\ttxt}[1]{ - \NameLeftContentRight{#1}{ + \NameLeftContentRight{\fqname:#1}{ \begin{ttext}[#1:desc] ##1 \end{ttext} @@ -188,25 +189,92 @@ % % QUANTITY % -\newenvironment{quantity}[5]{ - % key, symbol, si unit, si base units, comment (key to translation) + +% units: siunitx units arguments, possibly chained by '=' +% returns: 1\si{unit1} = 1\si{unit2} = ... +\directlua{ + function split_and_print_units(units) + if units == nil then + tex.print("1") + return + end + + local parts = {} + for part in string.gmatch(units, "[^=]+") do + table.insert(parts, part) + end + local result = "" + for i, unit in ipairs(parts) do + if i > 1 then result = result .. " = " end + result = result .. "\\SI{1}{" .. unit .. "}" + end + tex.print(result) + end +} +\newenvironment{quantity}[4]{ + % key, symbol, si unit(s), comment (key to global translation) \newcommand{\desc}[3][english]{ % language, name, description - \DT[qty:#1]{}{##1}{##2} + % \DT[qty:#1]{##1}{##2} + % \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}} + \DT[qty:#1]{##1}{##2} \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}} } - - \edef\qtyname{#1} - \edef\qtysign{#2} - \edef\qtyunit{#3} - \edef\qtybaseunits{#4} - \edef\qtycomment{#5} + % TODO put these in long term key - value storage for generating a full table and global referenes \qtyRef + % for references, there needs to be a label somwhere + \edef\qtyname{qty:#1} + \edef\qtydesc{qty:#1_desc} + \def\qtysymbol{#2} + \def\qtyunits{#3} + \edef\qtycomment{#4} } { - Quantity: \expandafter\GT\expandafter{qty:\qtyname}: \GT{qty:\qtyname_desc} \\ - $\qtysign$ $[\SI{\qtyunit}] = [\SI{\qtybaseunits}]$ - \qtycomment \\ + \NameLeftContentRight{\qtyname}{ + \begingroup + Symbol: $\qtysymbol$ + \IfTranslationExists{\qtydesc}{ + \\Description: \GT{\qtydesc} + }{} + \\Unit: $\directlua{split_and_print_units([[\qtyunits]])}$ + \expandafter\IfTranslationExists\expandafter\qtycomment{ + \\Comment: \GT\qtycomment + }{\\No comment \color{gray}} + \label{\qtyname} + \endgroup + } \ignorespacesafterend + + % for TOC + \refstepcounter{quantity}% + \addquantity{\expandafter\gt\expandafter{\qtyname}}% + % \noindent\textbf{My Environment \themyenv: #1}\par% } +\newcounter{quantity} +\Eng[list_of_quantitites]{List of quantitites} +\Ger[list_of_quantitites]{Liste von Größen} +\newcommand{\listofquantities}{% + \section*{\GT{list_of_quantitites}}% + \addcontentsline{toc}{section}{\GT{list_of_quantitites}}% + \par\noindent\hrule\par\vspace{0.5\baselineskip}\@starttoc{myenv}% +} +\newcommand{\addquantity}[1]{\addcontentsline{quantity}{subsection}{\protect\numberline{\themyenv}#1}} + +% Custon environment with table of contents, requires etoolbox? +% Define a custom list +\newcommand{\listofmyenv}{% + \section*{List of My Environments}% + \addcontentsline{toc}{section}{List of My Environments}% + \par\noindent\hrule\par\vspace{0.5\baselineskip}\@starttoc{myenv}% +} +\newcommand{\addmyenv}[1]{\addcontentsline{myenv}{subsection}{\protect\numberline{\themyenv}#1}} +% Define the custom environment +\newcounter{myenv} +\newenvironment{myenv}[1]{% + \refstepcounter{myenv}% + \addmyenv{#1}% + \noindent\textbf{My Environment \themyenv: #1}\par% +}{\par\vspace{0.5\baselineskip}} + @@ -226,7 +294,7 @@ \directlua{ local cases = { pdf = "eq:pt:distributions:pdf", - pmf = "eq:pt:distributions:pdf", + pmf = "eq:pt:distributions:pmf", cdf = "eq:pt:distributions:cdf", mean = "eq:pt:mean", variance = "eq:pt:variance" diff --git a/src/util/macros.tex b/src/util/macros.tex index 46ace73..e593c40 100644 --- a/src/util/macros.tex +++ b/src/util/macros.tex @@ -4,7 +4,9 @@ \def\Grad{\vec{\nabla}} \def\Div{\vec{\nabla} \cdot} \def\Rot{\vec{\nabla} \times} +% common vectors \def\vecr{\vec{r}} +\def\vecx{\vec{x}} \def\kB{k_\text{B}} \def\EFermi{E_\text{F}} diff --git a/src/util/translation.tex b/src/util/translation.tex index 7ba9e2a..58a12a0 100644 --- a/src/util/translation.tex +++ b/src/util/translation.tex @@ -18,11 +18,17 @@ \newcommand{\gt}[1]{\expandafter\GetTranslation\expandafter{\fqname:#1}} \newcommand{\GT}[1]{\expandafter\GetTranslation\expandafter{#1}} -\newcommand{\IfTranslationExists}{ - % \IfTranslation{\languagename} - \IfTranslation{english} % only check english. All translations must be defined for english +\newcommand{\IfTranslationExists}[1]{ + % \IfTranslation{english}{#1}%{#2}{#3} % only check english. All translations must be defined for english + % \edef\arg{#1} + \def\tempiftranslation{\IfTranslation{english}} + \expandafter\tempiftranslation\expandafter{#1} % only check english. All translations must be defined for english + % {S\color{red}\arg END} + % \IfTranslation{english}{\arg} % only check english. All translations must be defined for english +} +\newcommand{\iftranslation}[3]{ + \IfTranslationExists{\fqname:#1}{#2}{#3} } -\newcommand{\iftranslation}[1]{\expandafter\IfTranslationExists\expandafter{\fqname:#1}} % Define a translation and also make the fallback if it is the english translation % 1: lang, 2: key, 3: translation @@ -46,11 +52,13 @@ } } } -\newcommand{\DT}[3][\fqname]{ +% Define a new translation +% [1]: key, 2: lang, 3: translation +\newcommand{\DT}[3][dummy]{ \ifstrempty{#3}{}{ % dont add empty translations so that the fallback will be used instead % hack because using expandafter on the second arg didnt work \def\tempaddtranslation{\addtranslationcustom{#2}} - \ifstrequal{#1}{\fqname}{ + \ifstrequal{#1}{dummy}{ \expandafter\tempaddtranslation\expandafter{\fqname}{#3} }{ \expandafter\tempaddtranslation\expandafter{#1}{#3}